I was wondering, when the time comes, will my ant colony produce queens and males? I keep a colony in a formicarium, and do captive colonies produce queens and males, and if so, what should I do with them when they appear?

Yes, they will produce alates, but so long as they aren't subject to air from outside, the alates won't try to fly away. The reason for this is that ant colonies naturally coordinate nuptial flights via pheromones (which are in the air around colonies). If your ant colony doesn't have any other colony of the same species to coordinate with, they won't send their alates out. I hope that made sense.

the queens eventually shed there wings and act as big workers and the males die. Just in case I would put a lid or something on since the rare occasion the might fly you don't have to worry about ants infesting your house